Structure-preserving weighted BDF2 methods for Anisotropic Cahn-Hilliard model: uniform/variable-time-steps

2024/04/20 by Meng Li, Li, Meng, Jingjiang Bi +3 · 1 citation
Materials Science · Mathematics · Engineering · #Solidification and crystal growth phenomena #Differential Equations and Numerical Methods #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2404.13259

Abstract

In this paper, we innovatively develop uniform/variable-time-step weighted and shifted BDF2 (WSBDF2) methods for the anisotropic Cahn-Hilliard (CH) model, combining the scalar auxiliary variable (SAV) approach with two types of stabilized techniques. Using the concept of G-stability, the uniform-time-step WSBDF2 method is theoretically proved to be energy-stable. Due to the inapplicability of the relevant G-stability properties, another technique is adopted in this work to demonstrate the energy stability of the variable-time-step WSBDF2 method. In addition, the two numerical schemes are all mass-conservative.Finally, numerous numerical simulations are presented to demonstrate the stability and accuracy of these schemes.

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• A second-order generalized BDF method for the two-dimensional (modified) Fisher-Kolmogorov-Petrovsky-Piskunov equation

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